Finite Group Databasebeta

← #11786671

Subgroups — #11786671

Order 1152.

906 conjugacy classes of subgroups; only the 191 normal subgroups are shown.

normal subgroups only

This group has 906 conjugacy classes of subgroups — too many to draw. Only its 191 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10595975C211yesmaximal, characteristic
2C32×#384C211yesmaximal, characteristic, complemented
3#10592665C211yesmaximal, characteristic
4#10592663C211yesmaximal, characteristic, complemented
5C2×#63632C211yesmaximal, characteristic
6#10589396C211yesmaximal, characteristic, complemented
7#10589389C211yesmaximal, characteristic, complemented
8#69592—34nomaximal
9C2×#3828C2211yescharacteristic
10C2×C32×C4⋊C4—22no—
11C2×C32×C4⋊C4C2211yescharacteristic
12C2×C32×C4⋊C4C2211yescharacteristic
13C2×C32×C42C2211yescharacteristic
14C4×#638—22no—
15#64135C2211yescharacteristic
16C2×#3748C2211yescharacteristic
17C2×#3748C2211yescharacteristic
18#64102—21no—
19#64101—21no—
20C4⋊C4×C3⋊D3—21no—
21#64096—21no—
22#63637—21no—
23#63636—21no—
24#63635—21no—
25#63634—21no—
26#63632C414yescomplemented
27#5504—34no—
28C3×#384D314yescomplemented
29#4966—34no—
30#4964—34no—
31C2×#805—34no—
32#4530—34no—
33#4523—34no—
34C22×C32×C4—21no—
35C22×C32×C4—21no—
36C22×C32×C4D412yes—
37C22×C32×C4C2311yescharacteristic
38C2×#638—21no—
39#3828—21no—
40#3828—21no—
41#3828C2×C412yes—
42#3828Q812yes—
43C2×C4⋊(C3⋊D3)D411yescharacteristic
44C2×C4×C3⋊D3—21no—
45C2×C4×C3⋊D3—22no—
46C2×#634D411yescharacteristic
47C32×C4⋊C4—21no—
48C32×C4⋊C4—21no—
49C32×C4⋊C4—21no—
50C32×C4⋊C4—21no—
51C32×C4⋊C4—44no—
52C32×C42—21no—
53C32×C42C2×C412yescomplemented
54#3757—21no—
55#3752—22no—
56C4⋊(C3⋊Dic3)D411yescharacteristic
57C4⋊(C3⋊Dic3)D411yescharacteristic
58#3750—22no—
59C4×C3⋊Dic3—22no—
60C4×C3⋊Dic3—21no—
61#3748—21no—
62#3748—21no—
63#3748—21no—
64#3748C2×C412yescomplemented
65C2×C3⋊(C3⋊C8)—21no—
66C2×C3⋊(C3⋊C8)—21no—
67#1859—91noSylow
68C2×#235—34no—
69C2×C3×C4⋊C4—28no—
70C2×C3×C4⋊C4C2×D314yes—
71C2×C3×C4⋊C4C2×D314yes—
72C2×C3×C42C2×D314yes—
73C4×#67—68no—
74#926—34no—
75C2×#208—34no—
76C2×#208—34no—
77#893—64no—
78#892—64no—
79D3×C4⋊C4—64no—
80#887—64no—
81#810—64no—
82#809—64no—
83#808—64no—
84#807—64no—
85#805—316no—
86C23×C32C2×D411yescharacteristic
87C22×C3⋊D3—21no—
88C2×C32×C4—22no—
89C2×C32×C4—22no—
90C2×C32×C4—22no—
91C2×C32×C4—22no—
92C2×C32×C4—42no—
93C2×C32×C4—42no—
94C2×C32×C4—41no—
95C2×C32×C4C22×C411yescharacteristic
96C2×C32×C4C2×D411yescharacteristic
97C2×C32×C4C2×D411yescharacteristic
98C2×C32×C4C2×Q811yescharacteristic
99C2×C32×C4#4111yescharacteristic
100C2×C32×C4#4111yescharacteristic
101#638—22no—
102#638—22no—
103C2×C3⋊Dic3—21no—
104C2×C3⋊Dic3—21no—
105C2×C3⋊Dic3—21no—
106C4⋊(C3⋊D3)—21no—
107C4⋊(C3⋊D3)C4⋊C412yescomplemented
108C4×C3⋊D3—22no—
109C4×C3⋊D3—22no—
110C4×C3⋊D3—82no—
111#634—21no—
112#634C4⋊C412yescomplemented
113C3⋊(C3⋊C8)—22no—
114C3⋊(C3⋊C8)—41no—
115#520—91no—
116#428—91no—
117C2×#104—91no—
118#417—91no—
119#384C3⋊D311yescharacteristic, complemented
120#343—91no—
121#339—91no—
122C22×C3×C4—24no—
123C22×C3×C4—24no—
124C22×C3×C4#6718yes—
125C22×C3×C4C22×D314yes—
126C2×#67—64no—
127#235—38no—
128#235—38no—
129#235—64no—
130#235—64no—
131C2×D12—34no—
132C2×C4×D3—64no—
133C2×C4×D3—68no—
134C2×Dic6—34no—
135C3×C4⋊C4—24no—
136C3×C4⋊C4—24no—
137C3×C4⋊C4—24no—
138C3×C4⋊C4—24no—
139C3×C4⋊C4—416no—
140C3×C42—24no—
141C3×C42C4×D318yescomplemented
142#217—64no—
143(C2×D3)⋊C4—68no—
144C4⋊Dic3—34no—
145C4⋊Dic3—34no—
146Dic3⋊C4—68no—
147C4×Dic3—68no—
148C4×Dic3—64no—
149#208—38no—
150#208—64no—
151#208—64no—
152#208—64no—
153C2×C3⋊C8—64no—
154C2×C3⋊C8—64no—
155C22×C32—21no—
156C22×C32—21no—
157C22×C32C4×D411yescharacteristic
158C22×C32#12011yescharacteristic
159C22×C32C22⋊Q811yescharacteristic
160C2×C3⋊D3—22no—
161C2×C3⋊D3—41no—
162C2×C3⋊D3—41no—
163C32×C4—24no—
164C32×C4—42no—
165C32×C4—81no—
166C32×C4C2×C4⋊C411yescharacteristic
167C32×C4C4×D411yescharacteristic
168C32×C4C22⋊Q811yescharacteristic
169C32×C4#12311yescharacteristic
170C3⋊Dic3—22no—
171C3⋊Dic3—41no—
172C3⋊Dic3—41no—
173C2×#41—91no—
174C2×M16—91no—
175C2×M16—91no—
176C4×Q8—181no—
177C4×D4—181no—
178C4×D4—182no—
179#117—91no—
180#117—181no—
181C2×C4⋊C4—22no—
182C2×C4⋊C4—181no—
183C2×C4⋊C4C2×C3⋊D311yescharacteristic
184C2×C4⋊C4C2×C3⋊D311yescharacteristic
185C2×C42C2×C3⋊D311yescharacteristic
186#107—181no—
187#106—181no—
188#104—94no—
189#103—181no—
190#102—181no—
191C23×C3C2×#6714yes—
192C22×D3—64no—
193C2×C3×C4—28no—
194C2×C3×C4—28no—
195C2×C3×C4—28no—
196C2×C3×C4—28no—
197C2×C3×C4—48no—
198C2×C3×C4—48no—
199C2×C3×C4—44no—
200C2×C3×C4C2×C4×D314yes—
201C2×C3×C4#23514yes—
202C2×C3×C4D3×D414yes—
203C2×C3×C4D3×D414yes—
204C2×C3×C4D3×Q814yes—
205C2×C3×C4#23914yes—
206#67—68no—
207#67—68no—
208C2×Dic3—64no—
209C2×Dic3—64no—
210C2×Dic3—64no—
211D12—38no—
212D12—64no—
213C4×D3—68no—
214C4×D3—68no—
215C4×D3—248no—
216Dic6—38no—
217Dic6—64no—
218C3⋊C8—68no—
219C3⋊C8—124no—
220C2×C32—21no—
221C2×C32—21no—
222C2×C32#38511yescharacteristic
223C2×C32#45311yescharacteristic
224C2×C32#45611yescharacteristic
225C3⋊D3—42no—
226#41—92no—
227#41—92no—
228#41—181no—
229#41—181no—
230C2×Q8—91no—
231C2×D4—91no—
232C2×D4—181no—
233C22×C4—21no—
234C22×C4—21no—
235C22×C4—182no—
236C22×C4—181no—
237C22×C4#63812yes—
238C22×C4C22×C3⋊D311yescharacteristic
239M16—92no—
240M16—181no—
241M16—181no—
242M16—181no—
243C2×C8—181no—
244C2×C8—181no—
245C4⋊C4—21no—
246C4⋊C4—21no—
247C4⋊C4—21no—
248C4⋊C4—21no—
249C4⋊C4—44no—
250C4⋊C4—91no—
251C4⋊C4—91no—
252C4⋊C4—182no—
253C22⋊C4—182no—
254C22⋊C4—181no—
255C42—21no—
256C42—182no—
257C42—181no—
258C42C4×C3⋊D312yescomplemented
259C22×C3—24no—
260C22×C3—24no—
261C22×C3C4×#6714yes—
262C22×C3#93714yes—
263C22×C3#94614yes—
264C2×D3—68no—
265C2×D3—124no—
266C2×D3—124no—
267C3×C4—216no—
268C3×C4—48no—
269C3×C4—84no—
270C3×C4D3×C4⋊C414yes—
271C3×C4#89314yes—
272C3×C4#89414yes—
273C3×C4#89614yes—
274Dic3—68no—
275Dic3—124no—
276Dic3—124no—
277C32#185911yescharacteristic, complemented, Sylow
278C23—181no—
279C23C2×#63811yescharacteristic
280Q8—92no—
281Q8—181no—
282D4—92no—
283D4—182no—
284D4—182no—
285D4—181no—
286C2×C4—22no—
287C2×C4—22no—
288C2×C4—22no—
289C2×C4—22no—
290C2×C4—42no—
291C2×C4—42no—
292C2×C4—41no—
293C2×C4—181no—
294C2×C4—182no—
295C2×C4—182no—
296C2×C4—181no—
297C2×C4—181no—
298C2×C4—722no—
299C2×C4C2×C4×C3⋊D311yescharacteristic
300C2×C4#382811yescharacteristic
301C2×C4D4×C3⋊D311yescharacteristic
302C2×C4D4×C3⋊D311yescharacteristic
303C2×C4Q8×C3⋊D311yescharacteristic
304C2×C4#383211yescharacteristic
305C8—182no—
306C8—361no—
307C2×C3—24no—
308C2×C3—24no—
309C2×C3#498914yes—
310C2×C3#507714yes—
311C2×C3#509514yes—
312D3—128no—
313C22—21no—
314C22—21no—
315C22—182no—
316C22—361no—
317C22—361no—
318C22C4×#63811yescharacteristic
319C22#6414611yescharacteristic
320C22#6415511yescharacteristic
321C4—24no—
322C4—42no—
323C4—81no—
324C4—182no—
325C4—361no—
326C4—361no—
327C4C4⋊C4×C3⋊D311yescharacteristic
328C4#6410211yescharacteristic
329C4#6410311yescharacteristic
330C4#6410511yescharacteristic
331C3#6959214yescomplemented
332C2—21no—
333C2—21no—
334C2—362no—
335C2#1059268811yescharacteristic
336C2#1059277611yescharacteristic
337C2#1059279411yescharacteristic
subgroupG/H
centerC22#64146
commutatorC2×C32×C4C22×C4
FrattiniC22×C4C22×C3⋊D3
FittingC32×#384C2
socleC22×C32#120
prime radicalC2×#3828C22
cosocleC22×C32×C4C23
hypercenter#384C3⋊D3
hypocenterC32#1859
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4 ◁ #384

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
2. C32×#384C2semidirect
4. #10592663C2semidirect
6. #10589396C2semidirect
7. #10589389C2semidirect
26. #63632C4semidirect
28. C3×#384D3semidirect
53. C32×C42C2×C4semidirect
64. #3748C2×C4semidirect
107. C4⋊(C3⋊D3)C4⋊C4semidirect
112. #634C4⋊C4semidirect
119. #384C3⋊D3semidirect
141. C3×C42C4×D3semidirect
258. C42C4×C3⋊D3semidirect
277. C32#1859semidirect
331. C3#69592semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
#105959752
C32×#3842
#105926652
#105926632
C2×#636322
#105893962
#105893892
#695923